Abstract. 
The Burgers equation is one of the basic hydrodynamic models that
describes the evolution of velocity fields of sticky dust particles.
When supplied with random forcing it turns into an
infinite-dimensional random dynamical system that has been studied
since late 1990's. The variational approach to Burgers equation allows
to study the system by analyzing optimal paths in the random landscape
generated by random force potential. Therefore, this is essentially a
random media problem. For a long time only compact cases of Burgers
dynamics on the circle or a torus were understood well. In this talk,
I will discuss the quasi-compact case where the random forcing decays
to zero at infinity and the completely noncompact case of forcing that
is stationary in space-time. The main result is the description of the
ergodic components for the dynamics and One Force One Solution
principle on each of the components. Joint work with Eric Cator and
Kostya Khanin.